Critical value
From HandWiki
Short description: Mathematical values with different meanings by domain
Critical value may refer to:
- In differential topology, a critical value of a differentiable function ƒ : M → N between differentiable manifolds is the image (value of) ƒ(x) in N of a critical point x in M.[1]
- In complex dynamics, a critical value is the image of a critical point.
- In medicine, a critical value or panic value is a value of a laboratory test that indicates a serious risk to the patient.[2] Laboratory staff may be required to directly notify a physician or clinical staff of these values.
- In statistical hypothesis testing, the critical values of a statistical test are the boundaries of the acceptance region of the test.[3] The acceptance region is the set of values of the test statistic for which the null hypothesis is not rejected. Depending on the shape of the acceptance region, there can be one or more than one critical value.
Suppose the data can be realized from an N(0,1) distribution. For example, with a chosen significance level α = 0.05, from the Z-table, a one-tailed critical value of approximately 1.645 can be obtained. The one-tailed critical value Cα ≈ 1.645 corresponds to the chosen significance level. The critical region [Cα, ∞) is realized as the tail of the standard normal distribution.
References
- ↑ do Carmo, Manfredo Perdigão (1976). Differential Geometry of Curves and Surfaces. Prentice Hall. ISBN 0-13-212589-7.
- ↑ "Laboratory Critical/Panic Value List". https://stanfordhealthcare.org/health-care-professionals/laboratory-critical-value-list.html.
- ↑ Hughes, Ann J.; Grawoig, Dennis E. (1971). Statistics: A Foundation for Analysis. Reading, Mass.: Addison-Wesley. p. 191. ISBN 0-201-03021-7. https://archive.org/details/trent_0116302260611.
External links
- Selected critical values of the Student's t distribution
- Selected upper critical values of the F distribution
- Selected upper critical values of the Chi-squared distribution
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